| /* ----------------------------------------------------------------------------- |
| * Robust variance for Cox proportional hazard survival regression |
| * -------------------------------------------------------------------------- */ |
| |
| --------------------------------------------------------------------------- |
| -- Data taken from survival package of R |
| --------------------------------------------------------------------------- |
| DROP TABLE IF EXISTS bladder; |
| CREATE TABLE bladder( |
| id INTEGER, |
| rx INTEGER, |
| num INTEGER, |
| sz INTEGER, |
| stop INTEGER, |
| event INTEGER, |
| enum INTEGER); |
| |
| COPY bladder FROM STDIN; |
| 1 1 1 3 1 0 1 |
| 1 1 1 3 1 0 2 |
| 1 1 1 3 1 0 3 |
| 1 1 1 3 1 0 4 |
| 2 1 2 1 4 0 1 |
| 2 1 2 1 4 0 2 |
| 2 1 2 1 4 0 3 |
| 2 1 2 1 4 0 4 |
| 3 1 1 1 7 0 1 |
| 3 1 1 1 7 0 2 |
| 3 1 1 1 7 0 3 |
| 3 1 1 1 7 0 4 |
| 4 1 5 1 10 0 1 |
| 4 1 5 1 10 0 2 |
| 4 1 5 1 10 0 3 |
| 4 1 5 1 10 0 4 |
| 5 1 4 1 6 1 1 |
| 5 1 4 1 10 0 2 |
| 5 1 4 1 10 0 3 |
| 5 1 4 1 10 0 4 |
| 6 1 1 1 14 0 1 |
| 6 1 1 1 14 0 2 |
| 6 1 1 1 14 0 3 |
| 6 1 1 1 14 0 4 |
| 7 1 1 1 18 0 1 |
| 7 1 1 1 18 0 2 |
| 7 1 1 1 18 0 3 |
| 7 1 1 1 18 0 4 |
| 8 1 1 3 5 1 1 |
| 8 1 1 3 18 0 2 |
| 8 1 1 3 18 0 3 |
| 8 1 1 3 18 0 4 |
| 9 1 1 1 12 1 1 |
| 9 1 1 1 16 1 2 |
| 9 1 1 1 18 0 3 |
| 9 1 1 1 18 0 4 |
| 10 1 3 3 23 0 1 |
| 10 1 3 3 23 0 2 |
| 10 1 3 3 23 0 3 |
| 10 1 3 3 23 0 4 |
| 11 1 1 3 10 1 1 |
| 11 1 1 3 15 1 2 |
| 11 1 1 3 23 0 3 |
| 11 1 1 3 23 0 4 |
| 12 1 1 1 3 1 1 |
| 12 1 1 1 16 1 2 |
| 12 1 1 1 23 1 3 |
| 12 1 1 1 23 0 4 |
| 13 1 3 1 3 1 1 |
| 13 1 3 1 9 1 2 |
| 13 1 3 1 21 1 3 |
| 13 1 3 1 23 0 4 |
| 14 1 2 3 7 1 1 |
| 14 1 2 3 10 1 2 |
| 14 1 2 3 16 1 3 |
| 14 1 2 3 24 1 4 |
| 15 1 1 1 3 1 1 |
| 15 1 1 1 15 1 2 |
| 15 1 1 1 25 1 3 |
| 15 1 1 1 25 0 4 |
| 16 1 1 2 26 0 1 |
| 16 1 1 2 26 0 2 |
| 16 1 1 2 26 0 3 |
| 16 1 1 2 26 0 4 |
| 17 1 8 1 1 1 1 |
| 17 1 8 1 26 0 2 |
| 17 1 8 1 26 0 3 |
| 17 1 8 1 26 0 4 |
| 18 1 1 4 2 1 1 |
| 18 1 1 4 26 1 2 |
| 18 1 1 4 26 0 3 |
| 18 1 1 4 26 0 4 |
| 19 1 1 2 25 1 1 |
| 19 1 1 2 28 0 2 |
| 19 1 1 2 28 0 3 |
| 19 1 1 2 28 0 4 |
| 20 1 1 4 29 0 1 |
| 20 1 1 4 29 0 2 |
| 20 1 1 4 29 0 3 |
| 20 1 1 4 29 0 4 |
| 21 1 1 2 29 0 1 |
| 21 1 1 2 29 0 2 |
| 21 1 1 2 29 0 3 |
| 21 1 1 2 29 0 4 |
| 22 1 4 1 29 0 1 |
| 22 1 4 1 29 0 2 |
| 22 1 4 1 29 0 3 |
| 22 1 4 1 29 0 4 |
| 23 1 1 6 28 1 1 |
| 23 1 1 6 30 1 2 |
| 23 1 1 6 30 0 3 |
| 23 1 1 6 30 0 4 |
| 24 1 1 5 2 1 1 |
| 24 1 1 5 17 1 2 |
| 24 1 1 5 22 1 3 |
| 24 1 1 5 30 0 4 |
| 25 1 2 1 3 1 1 |
| 25 1 2 1 6 1 2 |
| 25 1 2 1 8 1 3 |
| 25 1 2 1 12 1 4 |
| 26 1 1 3 12 1 1 |
| 26 1 1 3 15 1 2 |
| 26 1 1 3 24 1 3 |
| 26 1 1 3 31 0 4 |
| 27 1 1 2 32 0 1 |
| 27 1 1 2 32 0 2 |
| 27 1 1 2 32 0 3 |
| 27 1 1 2 32 0 4 |
| 28 1 2 1 34 0 1 |
| 28 1 2 1 34 0 2 |
| 28 1 2 1 34 0 3 |
| 28 1 2 1 34 0 4 |
| 29 1 2 1 36 0 1 |
| 29 1 2 1 36 0 2 |
| 29 1 2 1 36 0 3 |
| 29 1 2 1 36 0 4 |
| 30 1 3 1 29 1 1 |
| 30 1 3 1 36 0 2 |
| 30 1 3 1 36 0 3 |
| 30 1 3 1 36 0 4 |
| 31 1 1 2 37 0 1 |
| 31 1 1 2 37 0 2 |
| 31 1 1 2 37 0 3 |
| 31 1 1 2 37 0 4 |
| 32 1 4 1 9 1 1 |
| 32 1 4 1 17 1 2 |
| 32 1 4 1 22 1 3 |
| 32 1 4 1 24 1 4 |
| 33 1 5 1 16 1 1 |
| 33 1 5 1 19 1 2 |
| 33 1 5 1 23 1 3 |
| 33 1 5 1 29 1 4 |
| 34 1 1 2 41 0 1 |
| 34 1 1 2 41 0 2 |
| 34 1 1 2 41 0 3 |
| 34 1 1 2 41 0 4 |
| 35 1 1 1 3 1 1 |
| 35 1 1 1 43 0 2 |
| 35 1 1 1 43 0 3 |
| 35 1 1 1 43 0 4 |
| 36 1 2 6 6 1 1 |
| 36 1 2 6 43 0 2 |
| 36 1 2 6 43 0 3 |
| 36 1 2 6 43 0 4 |
| 37 1 2 1 3 1 1 |
| 37 1 2 1 6 1 2 |
| 37 1 2 1 9 1 3 |
| 37 1 2 1 44 0 4 |
| 38 1 1 1 9 1 1 |
| 38 1 1 1 11 1 2 |
| 38 1 1 1 20 1 3 |
| 38 1 1 1 26 1 4 |
| 39 1 1 1 18 1 1 |
| 39 1 1 1 48 0 2 |
| 39 1 1 1 48 0 3 |
| 39 1 1 1 48 0 4 |
| 40 1 1 3 49 0 1 |
| 40 1 1 3 49 0 2 |
| 40 1 1 3 49 0 3 |
| 40 1 1 3 49 0 4 |
| 41 1 3 1 35 1 1 |
| 41 1 3 1 51 0 2 |
| 41 1 3 1 51 0 3 |
| 41 1 3 1 51 0 4 |
| 42 1 1 7 17 1 1 |
| 42 1 1 7 53 0 2 |
| 42 1 1 7 53 0 3 |
| 42 1 1 7 53 0 4 |
| 43 1 3 1 3 1 1 |
| 43 1 3 1 15 1 2 |
| 43 1 3 1 46 1 3 |
| 43 1 3 1 51 1 4 |
| 44 1 1 1 59 0 1 |
| 44 1 1 1 59 0 2 |
| 44 1 1 1 59 0 3 |
| 44 1 1 1 59 0 4 |
| 45 1 3 2 2 1 1 |
| 45 1 3 2 15 1 2 |
| 45 1 3 2 24 1 3 |
| 45 1 3 2 30 1 4 |
| 46 1 1 3 5 1 1 |
| 46 1 1 3 14 1 2 |
| 46 1 1 3 19 1 3 |
| 46 1 1 3 27 1 4 |
| 47 1 2 3 2 1 1 |
| 47 1 2 3 8 1 2 |
| 47 1 2 3 12 1 3 |
| 47 1 2 3 13 1 4 |
| 48 2 1 3 1 0 1 |
| 48 2 1 3 1 0 2 |
| 48 2 1 3 1 0 3 |
| 48 2 1 3 1 0 4 |
| 49 2 1 1 1 0 1 |
| 49 2 1 1 1 0 2 |
| 49 2 1 1 1 0 3 |
| 49 2 1 1 1 0 4 |
| 50 2 8 1 5 1 1 |
| 50 2 8 1 5 0 2 |
| 50 2 8 1 5 0 3 |
| 50 2 8 1 5 0 4 |
| 51 2 1 2 9 0 1 |
| 51 2 1 2 9 0 2 |
| 51 2 1 2 9 0 3 |
| 51 2 1 2 9 0 4 |
| 52 2 1 1 10 0 1 |
| 52 2 1 1 10 0 2 |
| 52 2 1 1 10 0 3 |
| 52 2 1 1 10 0 4 |
| 53 2 1 1 13 0 1 |
| 53 2 1 1 13 0 2 |
| 53 2 1 1 13 0 3 |
| 53 2 1 1 13 0 4 |
| 54 2 2 6 3 1 1 |
| 54 2 2 6 14 0 2 |
| 54 2 2 6 14 0 3 |
| 54 2 2 6 14 0 4 |
| 55 2 5 3 1 1 1 |
| 55 2 5 3 3 1 2 |
| 55 2 5 3 5 1 3 |
| 55 2 5 3 7 1 4 |
| 56 2 5 1 18 0 1 |
| 56 2 5 1 18 0 2 |
| 56 2 5 1 18 0 3 |
| 56 2 5 1 18 0 4 |
| 57 2 1 3 17 1 1 |
| 57 2 1 3 18 0 2 |
| 57 2 1 3 18 0 3 |
| 57 2 1 3 18 0 4 |
| 58 2 5 1 2 1 1 |
| 58 2 5 1 19 0 2 |
| 58 2 5 1 19 0 3 |
| 58 2 5 1 19 0 4 |
| 59 2 1 1 17 1 1 |
| 59 2 1 1 19 1 2 |
| 59 2 1 1 21 0 3 |
| 59 2 1 1 21 0 4 |
| 60 2 1 1 22 0 1 |
| 60 2 1 1 22 0 2 |
| 60 2 1 1 22 0 3 |
| 60 2 1 1 22 0 4 |
| 61 2 1 3 25 0 1 |
| 61 2 1 3 25 0 2 |
| 61 2 1 3 25 0 3 |
| 61 2 1 3 25 0 4 |
| 62 2 1 5 25 0 1 |
| 62 2 1 5 25 0 2 |
| 62 2 1 5 25 0 3 |
| 62 2 1 5 25 0 4 |
| 63 2 1 1 25 0 1 |
| 63 2 1 1 25 0 2 |
| 63 2 1 1 25 0 3 |
| 63 2 1 1 25 0 4 |
| 64 2 1 1 6 1 1 |
| 64 2 1 1 12 1 2 |
| 64 2 1 1 13 1 3 |
| 64 2 1 1 26 0 4 |
| 65 2 1 1 6 1 1 |
| 65 2 1 1 27 0 2 |
| 65 2 1 1 27 0 3 |
| 65 2 1 1 27 0 4 |
| 66 2 2 1 2 1 1 |
| 66 2 2 1 29 0 2 |
| 66 2 2 1 29 0 3 |
| 66 2 2 1 29 0 4 |
| 67 2 8 3 26 1 1 |
| 67 2 8 3 35 1 2 |
| 67 2 8 3 36 0 3 |
| 67 2 8 3 36 0 4 |
| 68 2 1 1 38 0 1 |
| 68 2 1 1 38 0 2 |
| 68 2 1 1 38 0 3 |
| 68 2 1 1 38 0 4 |
| 69 2 1 1 22 1 1 |
| 69 2 1 1 23 1 2 |
| 69 2 1 1 27 1 3 |
| 69 2 1 1 32 1 4 |
| 70 2 6 1 4 1 1 |
| 70 2 6 1 16 1 2 |
| 70 2 6 1 23 1 3 |
| 70 2 6 1 27 1 4 |
| 71 2 3 1 24 1 1 |
| 71 2 3 1 26 1 2 |
| 71 2 3 1 29 1 3 |
| 71 2 3 1 40 1 4 |
| 72 2 3 2 41 0 1 |
| 72 2 3 2 41 0 2 |
| 72 2 3 2 41 0 3 |
| 72 2 3 2 41 0 4 |
| 73 2 1 1 41 0 1 |
| 73 2 1 1 41 0 2 |
| 73 2 1 1 41 0 3 |
| 73 2 1 1 41 0 4 |
| 74 2 1 1 1 1 1 |
| 74 2 1 1 27 1 2 |
| 74 2 1 1 43 0 3 |
| 74 2 1 1 43 0 4 |
| 75 2 1 1 44 0 1 |
| 75 2 1 1 44 0 2 |
| 75 2 1 1 44 0 3 |
| 75 2 1 1 44 0 4 |
| 76 2 6 1 2 1 1 |
| 76 2 6 1 20 1 2 |
| 76 2 6 1 23 1 3 |
| 76 2 6 1 27 1 4 |
| 77 2 1 2 45 0 1 |
| 77 2 1 2 45 0 2 |
| 77 2 1 2 45 0 3 |
| 77 2 1 2 45 0 4 |
| 78 2 1 4 2 1 1 |
| 78 2 1 4 46 0 2 |
| 78 2 1 4 46 0 3 |
| 78 2 1 4 46 0 4 |
| 79 2 1 4 46 0 1 |
| 79 2 1 4 46 0 2 |
| 79 2 1 4 46 0 3 |
| 79 2 1 4 46 0 4 |
| 80 2 3 3 49 0 1 |
| 80 2 3 3 49 0 2 |
| 80 2 3 3 49 0 3 |
| 80 2 3 3 49 0 4 |
| 81 2 1 1 50 0 1 |
| 81 2 1 1 50 0 2 |
| 81 2 1 1 50 0 3 |
| 81 2 1 1 50 0 4 |
| 82 2 4 1 4 1 1 |
| 82 2 4 1 24 1 2 |
| 82 2 4 1 47 1 3 |
| 82 2 4 1 50 0 4 |
| 83 2 3 4 54 0 1 |
| 83 2 3 4 54 0 2 |
| 83 2 3 4 54 0 3 |
| 83 2 3 4 54 0 4 |
| 84 2 2 1 38 1 1 |
| 84 2 2 1 54 0 2 |
| 84 2 2 1 54 0 3 |
| 84 2 2 1 54 0 4 |
| 85 2 1 3 59 0 1 |
| 85 2 1 3 59 0 2 |
| 85 2 1 3 59 0 3 |
| 85 2 1 3 59 0 4 |
| \. |
| |
| --------------------------------------------------------------------------- |
| -- no stratification |
| --------------------------------------------------------------------------- |
| drop table if exists bladder_coxph_out; |
| drop table if exists bladder_coxph_out_summary; |
| select coxph_train('bladder', 'bladder_coxph_out', 'stop', 'ARRAY[rx, sz, num]', 'event=1', NULL, NULL); |
| |
| select * from bladder_coxph_out; |
| select * from bladder_coxph_out_summary; |
| |
| -- robust variance |
| drop table if exists bladder_rv_coxph_out; |
| select robust_variance_coxph('bladder_coxph_out', 'bladder_rv_coxph_out'); |
| |
| SELECT assert( |
| relative_error(coef, ARRAY[-0.53838728618390019, -0.05439102328789678, 0.19234011205408327]) < 1e-6 AND |
| relative_error(loglikelihood, -589.06745420305799144) < 1e-6 AND |
| relative_error(std_err, ARRAY[0.19985872786736181, 0.06960069357280596, 0.04646488068044735]) < 1e-6 AND |
| relative_error(robust_se, ARRAY[0.19296810565837841, 0.07081459654480815, 0.04766700334445047]) < 1e-6 AND |
| relative_error(robust_z, ARRAY[-2.7900324996558528, -0.7680764410410881, 4.0350787454415480]) < 1e-6 AND |
| relative_error(robust_p, ARRAY[0.00527027509779776, 0.442441772410999, 0.0000545839882079013]) < 1e-6, |
| 'Cox Robust Variance Estimators (bladder w/o stratification): Wrong results' |
| ) FROM bladder_rv_coxph_out; |
| |
| -- cluster variance (id) |
| drop table if exists bladder_cv_coxph_out; |
| select clustered_variance_coxph('bladder_coxph_out', 'bladder_cv_coxph_out', 'id'); |
| |
| SELECT assert( |
| relative_error(coef, ARRAY[-0.53838728618390019, -0.05439102328789678, 0.19234011205408327]) < 1e-6 AND |
| relative_error(loglikelihood, -589.06745420305799144) < 1e-6 AND |
| relative_error(std_err, ARRAY[0.19985872786736181, 0.06960069357280596, 0.04646488068044735]) < 1e-6 AND |
| relative_error(clustered_se, ARRAY[0.29467251572845515, 0.08753417995257935, 0.06689308222921776]) < 1e-6 AND |
| relative_error(clustered_z, ARRAY[-1.8270699079381791, -0.6213689705822628, 2.8753363672943806]) < 1e-6 AND |
| relative_error(clustered_p, ARRAY[0.06768925905530210, 0.53435688328289499, 0.00403597282368529]) < 1e-6, |
| 'Cox Cluster Variance Estimators (bladder w/ cluster(id) w/o stratification): Wrong results' |
| ) FROM bladder_cv_coxph_out; |
| |
| -- cluster variance (id, enum) |
| drop table if exists bladder_cv_coxph_out; |
| select clustered_variance_coxph('bladder_coxph_out', 'bladder_cv_coxph_out', 'id, enum'); |
| |
| SELECT assert( |
| relative_error(coef, ARRAY[-0.53838728618390019, -0.05439102328789678, 0.19234011205408327]) < 1e-6 AND |
| relative_error(loglikelihood, -589.06745420305799144) < 1e-6 AND |
| relative_error(std_err, ARRAY[0.19985872786736181, 0.06960069357280596, 0.04646488068044735]) < 1e-6 AND |
| relative_error(clustered_se, ARRAY[0.19296810565837841, 0.07081459654480815, 0.04766700334445047]) < 1e-6 AND |
| relative_error(clustered_z, ARRAY[-2.7900324996558528, -0.7680764410410881, 4.0350787454415480]) < 1e-6 AND |
| relative_error(clustered_p, ARRAY[0.00527027509779776, 0.442441772410999, 0.0000545839882079013]) < 1e-6, |
| 'Cox Cluster Variance Estimators (bladder w/ cluster(id) + cluster(enum) w/o stratification): Wrong results' |
| ) FROM bladder_cv_coxph_out; |
| |
| |
| --------------------------------------------------------------------------- |
| -- with stratification |
| --------------------------------------------------------------------------- |
| drop table if exists bladder_coxph_out; |
| drop table if exists bladder_coxph_out_summary; |
| select coxph_train('bladder', 'bladder_coxph_out', 'stop', 'ARRAY[rx, sz, num]', 'event=1', 'enum', NULL); |
| |
| -- robust variance |
| drop table if exists bladder_rv_coxph_out; |
| select robust_variance_coxph('bladder_coxph_out', 'bladder_rv_coxph_out'); |
| |
| SELECT assert( |
| relative_error(coef, ARRAY[-0.57986081953852453, -0.05093865053703769, 0.20849139987047763]) < 1e-6 AND |
| relative_error(loglikelihood, -428.05790500373399254) < 1e-6 AND |
| relative_error(std_err, ARRAY[0.20117781307700300, 0.06966981665067325, 0.04691285708902546]) < 1e-6 AND |
| relative_error(robust_se, ARRAY[0.18929312730428571, 0.06364037833687450, 0.04464477664866482]) < 1e-6 AND |
| relative_error(robust_z, ARRAY[-3.0632956821850557, -0.8004140117992169, 4.6700065611530599]) < 1e-6 AND |
| relative_error(robust_p, ARRAY[0.00218913638636697, 0.423470965451148, 0.00000301190115603589]) < 1e-6, |
| 'Cox Robust Variance Estimators (bladder w/ stratification): Wrong results' |
| ) FROM bladder_rv_coxph_out; |
| |
| -- cluster variance |
| drop table if exists bladder_cv_coxph_out; |
| select clustered_variance_coxph('bladder_coxph_out', 'bladder_cv_coxph_out', 'id'); |
| |
| SELECT assert( |
| relative_error(coef, ARRAY[-0.57986081953852453, -0.05093865053703769, 0.20849139987047763]) < 1e-6 AND |
| relative_error(loglikelihood, -428.05790500373399254) < 1e-6 AND |
| relative_error(std_err, ARRAY[0.20117781307700300, 0.06966981665067325, 0.04691285708902546]) < 1e-6 AND |
| relative_error(clustered_se, ARRAY[0.30343529013002124, 0.09303573931640849, 0.06567477635846880]) < 1e-6 AND |
| relative_error(clustered_z, ARRAY[-1.9109867520355186, -0.5475170177752731, 3.1746038803768615]) < 1e-6 AND |
| relative_error(clustered_p, ARRAY[0.05600628340725960, 0.58402358222142303, 0.00150041173830195]) < 1e-6, |
| 'Cox Cluster Variance Estimators (bladder w/ cluster(id) w/ stratification): Wrong results' |
| ) FROM bladder_cv_coxph_out; |
